As presented in [1]}, the problem of matching a pair of graphs \(\mathcal {G}^{A}\)  and \(\mathcal {G}^{B}\)  requires the definition of an affinity matrix \(\mathbf {K}\)  to measure the similarity between each pair of nodes and edges. Given the node cardinality \(i = |\mathbf {n}^{A}_{i}|\) , and \(j = |\mathbf {n}^{B}_{j}|\) , the symmetric affinity matrix \(\mathbf {K} \in \mathbb {R}^{ij \times ij}\)  encodes the similarity between nodes along its diagonal elements, whereas the edges similarity is encoded in the off-diagonal ones. Given \(\mathbf {K}\) , the problem of graph matching consists in finding the optimal correspondence \(\mathbf {X}\)  between all the nodes (Fig. 1), so that a compatibility functional \(J(\mathbf {X})\)  is maximised with a quadratic assignment problem (QAP) [2]},
